THE LAWS OF CONDUCTION OF HEAT IN BAES. 79 



(April 15) with the last of the same bar naked (April 11), which were made in 

 almost similar circumstances, we notice the prodigious effect of the increased 

 radiation due to the paper casing. Though the heat at the origin may be con- 

 sidered as the same, at a distance of only three inches the temperature in the 

 second case was less by nearly 30° Cent. ; at thirty inches distance, the proper heat 

 of the bar was but one-half of what it was in Case I. ; at four feet, one-third ; and, 

 at eight feet, it had vanished in the second case, while it was still sensible in the 

 first. Fourthly, it may be remarked that in Case I. the bar scarcely fulfilled, as 

 to length, the implied condition of the experiment, which assumes that the 

 extreme end of the bar shall be sensibly of the temperature of the air. As o- 3 

 of heat remained at eight feet, and as the bar extended only a few inches beyond 

 that point, it would appear that the conducted heat was not absolutely dissipated 

 by radiation. The effect, which is to render the decrement of heat in the extreme 

 holes rather too slow, is, however, barely appreciable in the deductions. 



56. Graphical Interpolation of the Statical Experiments. — As it was desirable to 

 combine the results of the independent experiments in each of the three Cases, 

 and to deduce the most probable temperature for any point of the bar, a graphical 

 method was adopted as follows : — Large sheets of drawing-paper were provided 

 covered with engraved squares one-tenth of an inch in the side. A horizontal 

 line was taken to represent the distances reckoned along the bar on a scale of four 

 inches to a foot, and at the proper intervals the observed temperatures (or rather 

 excesses of temperature) were set off as vertical ordinates on a scale of 10° to 1 

 inch. The general arrangement of the observations in this way is shown in Plate 

 III. on a reduced scale for Case I. 



57. It is plain, however, that this primary projection could only apply to a single 

 and comparable series of observations under each Case of Table I., since the tem- 

 perature of the origin might vary from one experiment to another. One set under 

 each Case was assumed as a standard series to which the others were to be referred. 

 In Case I., April 11 ; in Case II., April 15 ; in Case III., January 11 (b). But as 

 it is plain that for one and the same bar the curve of temperature has the same 

 form, though it may deviate in position to the right or left along the bar, each of 

 the other days' observations was separately projected on transparent cloth, and 

 then laid on the engraved squares over the first projection. By moving the system 

 of projected points to the right or left (taking care to keep the line of abscissae in 

 each case accurately coincident), a position was easily found where the points to 

 be interpolated accommodated themselves best to the general curvature of the 

 fundamental series. 



58. This method of interpolating independent series belonging to different funda- 

 mental temperatures has very great advantages. Had circumstances allowed me 

 to continue these observations, I should have applied it more extensively. A 

 clear instance of its utility will be seen by comparing the first and second row 



